Rfast (version 1.5)

MLE of the zero-inflated Poisson distribution: MLE of the zero-inflated Poisson distribution

Description

MLE of the zero-inflated Poisson distribution.

Usage

zip.mle(x, tol = 1e-09)

Arguments

x

A vector with discrete valued data.

tol

The tolerance level up to which the maximisation stops set to 1e-09 by default.

Value

A vector with three elements, the $\lambda$, $\pi$ (the proportion of excessive zeros) and the maximised log-likelihood.

Details

Instead of maximising the log-likelihood via a numerical optimiser we used a Newton-Raphson algorithm which is faster. See wikipedia for the equation to be solved. https://en.wikipedia.org/wiki/Zero-inflated_model In order to avoid negative values we have used link functions, log for the $lambda$ and logit for the $\pi$ as suggested by Lambert (1992).

References

Lambert Diane (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 34 (1): 1-14

Johnson Norman L., Kotz Samuel and Kemp Adrienne W. (1992). Univariate Discrete Distributions (2nd ed.). Wiley

See Also

poisson_only, colrange

Examples

x <- rpois(100, 2)
zip.mle(x)
sum( dpois(x, mean(x), log = TRUE) )  ## poisson log-likelihood
## small difference in the two log-likelihoods as expected.

x <- rpois(1000, 10)
x[ sample(1:1000, 100) ] <- 0
zip.mle(x)
sum( dpois(x, mean(x), log = TRUE) )  ## poisson log-likelihood
## significant difference in the two log-likelihoods.